Rambam is based on Nega’im 12:2, which states (based on Vayikra 14:45) that a house needs to be composed of stone, wood and earth in order to contract tzara’at impurity, and that marble does not count.
Tiferet Yisrael in Bo’az 3 explains that marble is never referred to as simply “stone” but instead “stones of marble”.
This is a purely speculative idea. But it's worth considering since you are looking for a "reason" behind the mitzvah and not a discussion of the halacha itself. Why is marble not considered like other stones.
Rambam distinguishes in this halacha between 2 categories, 1) "stones" (אבן) together with soil and wood and 2) "bricks"...